The Goodison Park outfit slipped to fifth in the Premier League table after Arsenal's 3-1 win over West Ham on Tuesday, but can climb back above their rivals if they avoid defeat against Crystal Palace on Wednesday.
Everton have qualified just once for the UEFA Champions League - in 2005 - and were knocked out in the qualifying rounds by Villarreal, whereas Arsenal are bidding to reach the competition for the 17th successive season.
But despite their lack of experience of qualifying for Europe's premier club competition, Martinez believes his side has the mental fortitude to hold off Arsene Wenger's men.
"You only decide games on technical, tactical and physical aspects when they don't mean much," he told the British media.
"When there is a real meaning in every point that you play for, psychologically you need to be very strong, and probably that's a big advantage that we have, and we've shown that in the last seven or eight weeks.
"When you get into a position like we are, it's a little bit unknown ground breaking through the points tally that we have.
"The team is focused, the football club is focused and we are very much all together fighting for the same aim.
"Psychologically we've got that winning mentality that you need."
